Quantum computing is a class of computing in which inherently quantum mechanical phenomena, such as quantum state superposition and entanglement, are harnessed to perform certain computations far more quickly than any classical computer could ever be capable of. In a “topological” quantum computer, calculations are performed by manipulating quasiparticles—called “non-abelian anyons”—that occur in certain physical systems. Anyons have unique physical characteristics that distinguish them from both fermions and bosons. Non-abelian anyons also have unique properties with respect to abelian anyons. It is these unique properties that serve as a basis for topological quantum computing, in which information is encoded as a topological property of non-abelian anyons; specifically the braiding of their space-time worldlines. This has certain benefits over other models of quantum computation. One key benefit is stability, as the quantum braiding is unaffected by perturbations on a scale that could cause error-inducing quantum decoherence in other types of quantum computer.
Broadly speaking, to date, two types of physical system have been considered as potential hosts of non-abelian anyons, namely “5/2 fractional quantum Hall” systems in condensed matter physics, and (more recently) semiconductor-superconductor (SE/SU) nanowires. With regard to the latter, a key advance in the field was the realization that non-abelian anyons, in the form of “Majorana zero modes” (MZMs), can be formed in regions of semiconductor (SE) coupled to a superconductor (SU). Based on this phenomenon, a network of SE/SU nanowires can be used to create a quantum bit, wherein each SE/SU nanowire comprises a length of semiconductor coated with a superconductor.
A quantum bit, or qubit, is an element upon which a measurement with two possible outcomes can be performed, but which at any given time (when not being measured) can in fact be in a quantum superposition of the two states corresponding to the different outcomes.
A “topological” qubit is a qubit implemented based on the above-mentioned technology of non-abelian anyons in the form of MZMs. A non-abelian anyon is a type of quasiparticle, meaning not a particle per se, but an excitation in an electron liquid that behaves at least partially like a particle. Particularly an anyon is a quasiparticle occurring in a two-dimensional system (two degrees of freedom in space). A Majorana zero mode is a particular bound state of such quasiparticles. Under certain conditions, these states can be formed in close to the semiconductor/superconductor interface in an SE/SU nanowire network, in a manner that enables them to be manipulated as quantum bits for the purpose of quantum computing. Regions or “segments” of the nanowire network between the MZMs are said to be in the “topological” regime.